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Shree Nayar

This course focuses on the recovery of the 3D structure of a scene from images taken from different viewpoints. We start by first building a comprehensive geometric model of a camera and then develop a method for finding (calibrating) the internal and external parameters of the camera model. Then, we show how two such calibrated cameras, whose relative positions and orientations are known, can be used to recover the 3D structure of the scene. This is what we refer to as simple binocular stereo. Next, we tackle the problem of uncalibrated stereo where the relative positions and orientations of the two cameras are unknown. Interestingly, just from the two images taken by the cameras, we can both determine the relative positions and orientations of the cameras and then use this information to estimate the 3D structure of the scene.

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This course focuses on the recovery of the 3D structure of a scene from images taken from different viewpoints. We start by first building a comprehensive geometric model of a camera and then develop a method for finding (calibrating) the internal and external parameters of the camera model. Then, we show how two such calibrated cameras, whose relative positions and orientations are known, can be used to recover the 3D structure of the scene. This is what we refer to as simple binocular stereo. Next, we tackle the problem of uncalibrated stereo where the relative positions and orientations of the two cameras are unknown. Interestingly, just from the two images taken by the cameras, we can both determine the relative positions and orientations of the cameras and then use this information to estimate the 3D structure of the scene.

Next, we focus on the problem of dynamic scenes. Given two images of a scene that includes moving objects, we show how the motion of each point in the image can be computed. This apparent motion of points in the image is called optical flow. Optical flow estimation allows us to track scene points over a video sequence. Next, we consider the video of a scene shot using a moving camera, where the motion of the camera is unknown. We present structure from motion that takes as input tracked features in such a video and determines not only the 3D structure of the scene but also how the camera moves with respect to the scene. The methods we develop in the course are widely used in object modeling, 3D site modeling, robotics, autonomous navigation, virtual reality and augmented reality.

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Syllabus

Getting Started: 3D Reconstruction - Multiple Viewpoints
Camera Calibration
Uncalibrated Stereo
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Optical Flow
Structure from Motion

Good to know

Know what's good
, what to watch for
, and possible dealbreakers
Introduces basic computer vision concepts and techniques
Focuses on 3D scene reconstruction from multiple viewpoints
Taught by Shree Nayar, a leading expert in computer vision
Provides hands-on practice through labs and assignments
Suitable for beginners in computer vision and image processing

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in 3D Reconstruction - Multiple Viewpoints with these activities:
Review linear algebra
Review the basics of linear algebra, such as matrix operations, vector spaces, and linear transformations, to strengthen your understanding of the mathematical concepts used in this course.
Browse courses on Linear Algebra
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  • Review your notes and textbooks from previous linear algebra courses.
  • Practice solving problems involving matrix operations, such as matrix multiplication and matrix inversion.
  • Review the concepts of vector spaces, including vector addition and scalar multiplication.
  • Study the properties of linear transformations, such as linearity and invertibility.
Read 'Computer Vision: Algorithms and Applications'
This book provides a comprehensive overview of computer vision algorithms and techniques, including those used in this course, to reinforce your understanding of the theoretical foundations.
View Computer Vision on Amazon
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  • Read the relevant chapters that cover the topics discussed in the course.
  • Take notes and highlight important concepts.
  • Solve the practice problems at the end of each chapter.
Follow tutorials on implementing 3D reconstruction algorithms
Follow online tutorials or workshops that provide step-by-step instructions on implementing 3D reconstruction algorithms using programming languages like Python and libraries like OpenCV, to gain hands-on experience in coding these techniques.
Browse courses on 3D Reconstruction
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  • Identify online tutorials or workshops that align with the topics covered in the course.
  • Follow the instructions and implement the algorithms in a programming environment.
  • Test the implemented algorithms on sample datasets or your own images.
Two other activities
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Solve 3D reconstruction problems
Practice solving problems related to 3D reconstruction using techniques such as camera calibration, structure from motion, and optical flow, to improve your understanding of the algorithms and their applications.
Browse courses on 3D Reconstruction
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  • Find online resources or textbooks that provide practice problems on 3D reconstruction.
  • Attempt to solve the problems independently, using the concepts and techniques covered in the course.
  • Check your solutions against provided solutions or discuss them with classmates or online forums.
Build a 3D model using photogrammetry
Create a 3D model of an object using photogrammetry techniques, such as capturing multiple images of the object from different angles and using software to generate a 3D model, to gain practical experience in 3D reconstruction.
Browse courses on Photogrammetry
Show steps
  • Choose an object to model and capture a series of photographs from various perspectives.
  • Use photogrammetry software or online services to process the images and generate a 3D model.
  • Refine and optimize the 3D model by editing the mesh or applying textures.

Career center

Learners who complete 3D Reconstruction - Multiple Viewpoints will develop knowledge and skills that may be useful to these careers:
Game Developer
Game Developers design, develop, and test video games. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for creating realistic and detailed video games.
Robotics Engineer
Robotics Engineers design, develop, and test robots. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for designing and developing robots that can see and interpret their environment.
3D Animator
3D Animators create 3D animations for use in movies, video games, and other applications. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for creating realistic and detailed 3D animations.
Technical Artist
Technical Artists create and manage the technical aspects of 3D models and animations for use in movies, video games, and other applications. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for creating realistic and detailed 3D models and animations.
Motion Capture Artist
Motion Capture Artists capture and process motion data for use in movies, video games, and other applications. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for capturing and processing motion data.
Computer Vision Engineer
Computer Vision Engineers design, develop, and test computer vision systems that can see and interpret images and videos like humans do. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a solid foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for designing and developing computer vision systems.
Computer Graphics Artist
Computer Graphics Artists create computer-generated images and animations for use in movies, video games, and other applications. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for creating realistic and detailed computer-generated images and animations.
3D Artist
3D Artists create 3D models and animations for use in movies, video games, and other applications. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for creating realistic and detailed 3D models and animations.
Autonomous Vehicle Engineer
Autonomous Vehicle Engineers design, develop, and test autonomous vehicles. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for designing and developing autonomous vehicles that can see and interpret their environment.
Virtual Reality Engineer
Virtual Reality Engineers design, develop, and test virtual reality systems. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for designing and developing virtual reality systems.
Photogrammetrist
Photogrammetrists create 3D models from photographs. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for creating realistic and detailed 3D models from photographs.
Augmented Reality Engineer
Augmented Reality Engineers design, develop, and test augmented reality systems. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for designing and developing augmented reality systems.
Virtual Tour Photographer
Virtual Tour Photographers create virtual tours of real-world locations using 360-degree cameras. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for creating realistic and detailed virtual tours.
3D Scanner Operator
3D Scanner Operators use 3D scanners to create 3D models of real-world objects. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for creating realistic and detailed 3D models using 3D scanners.
Drone Mapping Technician
Drone Mapping Technicians use drones to create maps and 3D models of real-world locations. The course on 3D Reconstruction - Multiple Viewpoints may be useful as it provides a foundation in the principles and techniques of 3D reconstruction from multiple images. This course will help you build a foundation in camera calibration, uncalibrated stereo, optical flow, and structure from motion, which are essential concepts for creating realistic and detailed maps and 3D models using drones.

Reading list

We've selected nine books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in 3D Reconstruction - Multiple Viewpoints.
Is the foundational text for multiple-view geometry, the mathematical foundation for many of the topics covered in this course. While the book is generally more of a reference, the sections on camera calibration, stereo calibration, optical flow, and structure from motion will be particularly valuable as a supplement.
Is an advanced textbook on computer vision with a focus on algorithms and applications. It provides excellent coverage of the topics in this course, with a particular focus on practical applications. This book would be a great supplementary text for students who want to learn more about these techniques in practice.
Comprehensive and practical guide to digital image processing, providing a solid foundation for the image processing techniques used in this course. It covers a wide range of topics, from image enhancement and filtering to image segmentation and object recognition. This book would be a great supplementary text for students who want to learn more about the image processing techniques used in this course.
Comprehensive overview of probabilistic robotics, providing a solid foundation for the robotics techniques used in this course. It covers a wide range of topics, from localization and mapping to planning and control. This book would be a great supplementary text for students who want to learn more about the robotics techniques used in this course.
Provides a more practical and industry-focused look at mobile robotics, focusing on the design, control, and implementation of autonomous mobile robots.
Provides a clear and concise introduction to computer vision algorithms and applications.

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